**4. Results and discussion**

#### **4.1 Validation**

The simulation results are presented for a typical VVER-1000 reactor with the specifications listed in **Table 1**. To evaluate simulation accuracy, the obtained results for solid fuel are compared with three other studies. Firstly, the distribution of the axial coolant temperature with 5 and 10 volume fractions of nanofluid is presented in **Figure 5**.

The obtained results are compared with the porous media approaches solved by Zarifi et al. [25]. In the research of Zarifi, the conservation equations are solved by numerical methods using visual FORTRAN language; Furthermore, the nanofluids analysis was compared with an analysis of pure water. Finally, the applied approaches in the Zarifi study were validated using the COBRA-EN code for pure water [25].

**Figure 5.** *Axial coolant temperature distribution in the solid fuel [13].*

*The Effect of Al2O3 Concentration in Annular Fuels for a Typical VVER-1000 Core DOI: http://dx.doi.org/10.5772/intechopen.105192*

#### **Figure 6.**

*Axial clad temperature distribution in the solid fuel [21].*

**Figure 7.** *Axial fuel temperature distribution in the solid fuel [22].*

Second, the distribution of the axial clad temperature in solid fuel with pure water is compared with the COBRA-EN code that Safaei has used (**Figure 6**) (In the simulation of Safaei, the COBRA-EN code is improved to make a thermal–hydraulic analysis for the VVER reactor. To validate it, this calculation is compared with reactor FSAR and analytical approaches.) [32].

Third, **Figure 7** presents the axial fuel temperature with 10 and 20 volume fractions of nanofluid. It is compared with the DRAGON/DONJON code used by Safarzadeh (In the simulation of Safarzadeh, the DRAGON, DONJON, and a thermal– hydraulic model are used for the coupled analysis of the nanofluid core. The results are compared with the final safety analysis report (FSAR).) [33].

Finally, as shown in **Figure 8**, the axial fuel temperature with pure water is demonstrated. It is evaluated with the plant's final safety analysis report (FSAR) [26].

**Figure 8.** *Axial fuel temperature distribution in the solid fuel [15].*

The comparison of the obtained results showed the calculations were in good agreement with other studies. Consequently, the accuracy of the validation is acceptable.

The results showed that due to the increase in heat transfer coefficient by increasing the concentration of Al2O3nanofluid, the coolant temperature increased, and the central fuel temperature decreased. It is observed that for 10% by volume of nanoparticles, the difference between the cooling temperature and pure water was about 21°C and the difference between the fuel temperature was about 26°C. This study describes the effect of nanofluid on the cooling system's performance in the reactor core.

#### **4.2 Results**

Here, it is simulated annular fuel with pure water. In annular fuel, heat is transferred from internal and external surfaces. **Figures 9** and **10** present the distribution

**Figure 9.** *Comparison of axial fuel temperature distribution.*

*The Effect of Al2O3 Concentration in Annular Fuels for a Typical VVER-1000 Core DOI: http://dx.doi.org/10.5772/intechopen.105192*

**Figure 10.** *Comparison of axial clad temperature distribution.*

of the fuel and clad temperature in annular fuel and solid fuel with pure water. As can be seen, the distribution of temperature would be cosine shaped, which is due to the cosine shape of the heat generated in the axial direction of the fuel rod.

As can be observed in **Figure 9**, the maximum value of the fuel temperature in solid and annular fuel is 1201 K and 1012 K, respectively. As observed, an approximately 16% reduction in peak temperature at the fuel center was due to the use of annular fuel instead of solid fuel. As shown in **Figure 10**, there is a difference of about 26 degrees between the clad temperature in the annular fuel and the solid fuel.

Furthermore, it simulated the annular fuel with nanofluid. Then, it is compared with pure water. **Figures 11** and **12** compare the distribution of the fuel and clad temperature in annular fuel with 10 and 20 volume nanofluid fractions with pure water.

**Figure 11.** *Comparison of axial fuel temperature distribution in the annular fuel.*

**Figure 12.** *Comparison of axial clad temperature distribution in the annular fuel.*

As can be seen in **Figure 11**, the maximum value of the fuel temperature in annular fuel with pure water is 1012 K, whereas the maximum value of the fuel temperature in annular fuel with 10 and 20 volume percentages of nanoparticles is 920 K and 885 K, respectively. It is concluded that by increasing the concentration of the nanofluid from *φ* ¼ 0*:*1 to*φ* ¼ 0*:*2, the decreasing peak temperature in the centre of the fuel changes from 9–13%. Also, **Figure 12** illustrates that there is about a 13 degrees reduction in the clad temperature with nanofluid compared to the clad temperature with pure water. It was also found that the clad temperature gets closer to the coolant temperature when the nanofluid concentration increases.

In annular fuel, the maximum fuel temperature is reduced because the heat is removed from both sides of the fuel rod. Furthermore, as the heat transfer surface increases, the value of heat flux decreases; thus, it increases the minimum departure from the nucleate boiling ratio (MDNBR) margin. Finally, by increasing the use of the annular fuel, the critical heat flux can be increased.

In the steady-state operational condition, the MDNBR is one of the key limitations of thermal–hydraulic safety. DNBR is calculated from the relation,

$$\text{DNBR} = \frac{\stackrel{\circ}{\text{q}}^{\circ}\_{\text{CHF}}}{\stackrel{\circ}{\text{q}}\_{\text{actual}}} \tag{8}$$

The nucleate boiling heat flux cannot be increased indefinitely, and it is called the critical heat flux (CHF) at some value. The reactor core must be designed to keep the DNBR larger than the minimum allowable value during steady-state operation, normal operational transients, and anticipated operational occurrences. In annular fuel, the minimum value of DNBR is 1.97, which is higher than the 1.75 value reported by the FSAR for the typical VVER-1000. In other words, the maximum actual heat flux in the annular fuel is 1389.93 kW/m<sup>2</sup> , while in FSAR, this value is equal to 1570 kW/m<sup>2</sup> [15].

According to the description, it was found that by using the nanofluid as a coolant, the heat generated in the core from the fission reaction in the fuel could be further

*The Effect of Al2O3 Concentration in Annular Fuels for a Typical VVER-1000 Core DOI: http://dx.doi.org/10.5772/intechopen.105192*

**Figure 13.** *Comparison of the core pressure drop in the annular fuel.*

transferred by the nanofluid. Therefore, safety margins are improved for various transient accidents and crashes.

As observed in **Figure 13** for the annular fuel, the pressure drop changes along the channel in different concentrations of nanoparticles. It is explained that as the concentration of nanofluids increases, the pressure drop increases.
